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PreprintCC BY 4.0arXiv

Iterated cotangent-difference integrals over totally real cyclotomic fields

  • Jin Cao
  • Hidekazu Furusho
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Abstract

We study iterated cotangent integrals with cyclotomic shifts and express their values along specified reference paths in terms of cyclotomic multiple zeta values. Differences of cotangent forms extend to a punctured projective line over a totally real cyclotomic field, giving a family of "real cyclotomic multiple zeta values." With rational tangential endpoints, these difference integrals are periods of mixed Tate motives over that field; integral endpoint data yield periods over its ring of integers after inverting primes dividing the level. The associated framed motivic classes generate a Hopf subalgebra under Goncharov's coproduct.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026iterated,
  title = {{Iterated cotangent-difference integrals over totally real cyclotomic fields}},
  author = {Jin Cao and Hidekazu Furusho},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04214},
  eprint = {2610.04214},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04214},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Iterated cotangent-difference integrals over totally real cyclotomic fields
AU  - Jin Cao
AU  - Hidekazu Furusho
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04214
UR  - https://arxiv.org/abs/2610.04214
AB  - We study iterated cotangent integrals with cyclotomic shifts and express their values along specified reference paths in terms of cyclotomic multiple zeta values. Differences of cotangent forms extend to a punctured projective line over a totally real cyclotomic field, giving a family of "real cyclotomic multiple zeta values." With rational tangential endpoints, these difference integrals are periods of mixed Tate motives over that field; integral endpoint data yield periods over its ring of integers after inverting primes dividing the level. The associated framed motivic classes generate a Hopf subalgebra under Goncharov's coproduct.
ER  -